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Ample vector bundles without Griffiths-semipositive metrics
Abstract
We construct a rank-two ample holomorphic vector bundle on an abelian surface that admits no smooth Griffiths-semipositive Hermitian metric, thereby giving a counterexample to the Griffiths conjecture. The proof combines a curvature obstruction that persists under deformations with the openness of ampleness in an irreducible moduli space of stable sheaves.
Related
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BibTeX
@misc{du2026ample,
title = {{Ample vector bundles without Griffiths-semipositive metrics}},
author = {Yun-Heng Du and Song-Yan Xie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26504},
eprint = {2609.26504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26504},
}
RIS
TY - UNPB
TI - Ample vector bundles without Griffiths-semipositive metrics
AU - Yun-Heng Du
AU - Song-Yan Xie
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26504
UR - https://arxiv.org/abs/2609.26504
AB - We construct a rank-two ample holomorphic vector bundle on an abelian surface that admits no smooth Griffiths-semipositive Hermitian metric, thereby giving a counterexample to the Griffiths conjecture. The proof combines a curvature obstruction that persists under deformations with the openness of ampleness in an irreducible moduli space of stable sheaves.
ER -